The title is a reference to the phrase "The Birds and the Bees" which is an English idiomatic expression that refers to courtship and sexual intercourse.
Bev has Slurm Loco, Slurm, Diet Slurm, Dr. Jitter, Mountain Goo, and Walrus Juice. These refer to Coke Classic, Coke, Diet Coke, Dr. Pepper, Mountain Dew, and Bug Juice.
The opening caption is a reference to the now famous Fry internet meme (taken from the episode "The Lesser of Two Evils"), which was also used in the promos for the new season. Another internet meme of Fry that was featured in the episode is the "Shut up and take my money" meme.
Parody of the Batman spotlight in the original Batman series.
Zoidberg says "To the Employment Cave!" which refers to the infamous phrase, "To the Batcave!". This reference goes along with the Batman spotlight reference.